Rule of Schulze and Hardy

Some of the pertinent interactions that affect colloid stability are readily apparent from Figs. 7.4 and 7.12. The main effect of electrolytes is a more rapid decay of the repulsion energy with distance and to compact the double layer (reducing k 1). Experimentally it is known that the charge of the counterion plays an important role. The critical electrolyte concentration required just to agglomerate the colloids is proportional to z 6 Aj for high surface potential, and to z 2 A, 2, at low potentials [(4) and (5) in Table 7.3]. This is the theoretical basis for the qualitative valency rule of Schulze and Hardy. 

J. Th. G. Overbeek, Strong and weak points in the interpretation of colloid stability, Adv. Colloid Interface Sci. 16 17 (1982) The rule of Schulze and Hardy, Pure Appl. Chem. 52 1151 (1980). 

The influence of counterion valence on the double layer thickness is described by the valency rule of Schulze and Hardy. It basically predicts that if a monovalent counterion is changed to a divalent counterion, the thickness of the double layer decreases by half and if the divalent counterion is changed to a trivalent ion, the thickness of the double layer decreases by three-quarters (Fig. 9.2). The relative amounts of counterions required to induce flocculation are 100 for a monovalent, 2 for a divalent, and 0.04 for a trivalent ion. 

Rule of Schulze and Hardy See Schulze-Hardy Rule. 

The flocculation values united in Tables I and II clearly demonstrate the well-known rule of Schulze and Hardy stating that the flocculation value is first of all determined by the valency of the ions which are oppositely charged to the particles of the sol, whereas the spvecific nature of these ions is far less important. The influence of the valency and. the nature of the ions bearing the same charge as the particles is of subordinate importance. 

In Part I the principles were discusseicl on which the interaction of colloidal particles may be understood, and by, way of application the case of the interaction of two parallel flat plates was dealt with in Part II. Starting from this case it was possible to form a picture of the behaviour of colloidal particles and to come to an understanding of such fundamental properties as stability, flocculation value and the rule of Schulze and Hardy. 

Although these concentrations are rather low, we already find a considerable spreading in the direction of the rule of Schulze and Hardy. In the approximative theory, working with the equations for small values of which the in-... 

The basic concepts of this theory were the mutual repulsion consequent upon the interaction of two electro-chemical double layers, and the attraction by the London—Van der Waals forces. The principal facts of stability could be explained by combining these two forces. Among other things, a quantitative explanation of the rule of Schulze and Hardy has been given. For this purpose it was essential to use the unapproximated G o u y—C h a p m a n equations for the double layer. The approximation of Debye and Hiickel, however useful in the theory of electrolytes, appears to have only a very limited applicability in colloid chemistry. 

The introduction of several refinements was necessary to explain various details. The quantitatieve agreement between theory and experiment, and the deviations from the rule of Schulze and Hardy (lyotropic effects) made it necessary to reckon explicitly with dimensions and the specific adsorbality of the ions. To this end. Stern s theory has been introduced. 

The influence of the valency and the concentration of the electrolytes agrees with experimental data as expressed by the rule of Schulze and Hardy. As a first approximation following from the theory we find that the flocculation values for monovalent, bivalent and trivalent electrolytes are in the proportion... 

This regularity is known as the rule of Schulze and Hardy and is illustrated in... 

Tabic 4, wberens larger tables are given in chapter VHI, 3, p 307. An influence of electrolytes according to the rule of Schulze and Hardy is not only found in flocculation values but also very clearly in electrokinetic phenomena and generally in all phenomena, where the electrical double layer plays an outstanding role. 

Exceptions to the rule of Schulze and Hardy occur when the counter ions arc of a kind to be specifically adsorbed (large organic ions) or to react chemically with the ions building up the double layer. 

This approximate differential equation (42) will in most cases not be suitable to describe colloidal phenomena, because the valencies of positive and negative ions occur in it in a symmetrical way through x, whereas experimentally, for instance in the rule of Schulze and Hardy, (Ch II, p 82) the influence of positive and negative ions is essentially different. 

The most outstanding feature of the stability of hydrophobic sols is the great influence of the valency of electrolytes, especially the counterions, as expressed by the rule of Schulze and Hardy (c/. chapter II, 5 c. 1, p. 81). Now in cq. (9) and (10) the valency of the electrolytes is completely expressed in the quantity x and there the roles of the valency of positive and negative ions are perfectly symmetrical. 

The most striking facts to be explained by a theory on the stability of hydrophobic colloids are the valency rule of Schulze and Hardy (see chapter II, 5 c, 1, p 81) and a certain relation between the stability and the -potential. Hardy already observed that a sol flocculates when it is nearly isoelectric with its surroundings, that is when the -potential is reduced to zero. Later investigations by Powis introduced the concept of a critical s-potential below which a sol flocculates and above which it is stable. This critical potential was found to be about 25-30 milli-vplts. The extension of the experimental material on one hand and the criticisms rised against the interpretation of electrophoresis measurements (see chapter V, 6b, p. 210) on the other, made the existence of a critical potential doubtful. Other quantities, connected with the electrolytic character of hydrophobic systems, have been proposed as governing the stability. Of these we mention the function introduced by Eilers and Korff and the activity coefficient / introduced by Wo. Ostwald In the theory of Verwey and Overbeek which will be set out in the next sections, the role of the -poten- tiai is less conspicuous although the electrical double layer remains of fundamental importance. 

STABILITY AND FLOCCULATION EXPLAINED BY POTENTIAL CURVES. RULE OF SCHULZE AND HARDY... 

It is imtnediately clear from this figure that the rule of Schulze and Hardy is satisfactorily explained. -g., for — 100 mV and A 2 the flocculation... 

In this section we shall especially pay attention to the rule of Schulze and Hardy... 

The ciirves for differem valencm are on the whole of the same slope, which points to a rather low value of y, lor v is proportional to z for low values of the surface poten-tiah In that case the observed slopes point to a value of u of the order of 10 cm, which is not in too had accord v/irh the measured values ol a, However if this is the right explanation, the rule of Schulze and Hardy cannot be understood because small values of Y lead to Ci Cg 1 ( )" instead of to 1 i (1) (see small print on p, 319). 

That this form of gelation is closely connected with coagulation is clearly proved by the fact that the concentrations of different electrolytes, necessary to bring about gelation, obey the rule of Schulze and Hardy (Table 12) and Table 13 shows the quasi-continuous transition from stability over gelation to flocculation. 

Just as it is usually more difficult to prepare stable sols than flocculated systems, there is more chance of obtaining a plastic or at least a flocculated system in preparing a concentrated suspension than a stable, dilatant one The agents promoting the flocculated state are the same as those for dilute colloidal systems and have been treated extensively in chapter VIII Wc only draw attention again to the influence of electrolytes in aqueous suspensions according to the rule of Schulze and Hardy (e chapter VIII, 10 a, p 335) ... 

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